On the lower bounds of the curvatures in a bounded domain

被引：0

作者：

LU Qi Keng ^{[1
]}

机构：

[1] Institute of Mathematics, Academy of Mathematics and Systems Science,Chinese Academy of Sciences

来源：

Science China Mathematics | 2015年 / 58卷 / 01期

基金：

中国国家自然科学基金;

关键词：

minimal function; minimal integral; lower bound;

D O I：

暂无

中图分类号：

O172.2 [积分学];

学科分类号：

0701 ; 070101 ;

摘要：

Let KD(z,z)be the Bergman kernel of a bounded domain D in Cnand SectD(z,ξ)and RicciD(z,ξ)be the holomorphic sectional curvature and Ricci curvature of the Bergman metric ds2=TDαβ(z,z)dzαdzβrespectively at the point z∈D with tangent vectorξ.It is proved by constructing suitable minimal functions that SectD(z,ξ)2-2 n+2n+1 KD1(z,z)TD1αβ(z,z)ξαξβKD2(z,z)TD2λμ(z,z)ξλξμ2and RicciD(z,ξ)n+1-(n+2)KD1(z,z)TD1(z,z)ξαξβKD2(z,z)TD2λμ(z,z)ξλξμ,where z∈D1DD2,D1is a ball contained in D and D2is a ball containing D.

引用

页码：1 / 10

页数：10

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